Question

Lim x->-2 x^3+8/x+2=

Answer 1

because ( (-2)³+8))/(-2+2)=0/0,

you use formula a³+b³°(a+b)(a²-ab+b²).

therefore (x³+8)/(x+2) = ( (x+2)(x²-2x+4))/(x+2) = x²-2x+4

so lim x->-2 (x²-2x+4) = (-2)²-2*(-2)+4=

=4+4+4=12.

Answer 2

Answer:

12

Step-by-step explanation:

note that x³ + 8 is a sum of cubes and factors as

x³ + 8 = (x + 2)(x² - 2x + 4), thus

lim x → - 2 $\frac{x^3+8}{x+2}$

= lim x → - 2 $\frac{(x+2)(x^2-2x+4)}{x+2}$

Cancel factor (x + 2) on numerator/denominator

= lim x → - 2 (x² - 2x + 4) ← evaluate by direct substitution

= (- 2)² - 2(- 2) + 4 = 4 + 4 + 4 = 12